Scala analysis: 617_T24
Aristoxenian style tetrachord 11/3 + 22/3 + 19, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 61.111 cents 61.111110 2: 183.333 cents 183.333330 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 316.6667 cents 316.6667 1: 61.1111 cents 61.1111 2: 122.2222 cents 122.2222 3: 316.6667 cents 316.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 61.11111 cents 1: 1 122.22222 cents 1: 1 316.66667 cents 2: 1 183.33333 cents 2: 1 377.77778 cents 2: 1 438.88889 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 61.1 183.3 500.0 61.1 : 122.2 438.9 500.0 183.3: 316.7 377.8 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 61.1111 .. 316.6667 cents 255.55556 cents 61.11111 cents 2: 183.3333 .. 438.8889 cents 255.55556 cents -133.33334 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 61.11111 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 316.66667 cents Average / Smallest step : 2.727273 Largest / Average step : 1.900000 Largest / Smallest step : 5.181818 Median interval of one step : 122.22222 cents, amount: 1 Least squares average step : 137.69841 cents, oct.: 413.09524 cents Scale is not proper Scale has trivalence property Scale is a mode of a 90-tone equal temperament with octave 500.000 cents degrees: 11 33 90 Least number of segments generator : 47 of 261.111 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 79 of 438.889 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 61.11111 cents Scale diversity : 0.933936 Lumma stability : 0.244444 Lumma impropriety factor : 0.266667 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 61.11111 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 36.5711 c. M: 61.1111 c. 5: 1 1 3 N M DE S SD: 24.4276 c. M:-38.8889 c. 6: 1 1 4 N M DE S SD: 16.0375 c. M:-22.2222 c. 7: 1 2 4 N T3 SD: 18.8370 c. M:-30.9524 c. 8: 1 2 5 N T3 SD: 2.5358 c. M:-4.1667 c. 25: 3 6 16 N T3 SD: 2.0286 c. M: 3.3333 c. 33: 4 8 21 N T3 SD: 0.9221 c. M: 1.5151 c. 41: 5 10 26 N T3 SD: 0.2474 c. M: 0.4065 c. 49: 6 12 31 N T3 SD: 0.2070 c. M:-0.3401 c. 90: 11 22 57 N T3 SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 77.9642 cents 6 x 7:8 S SD: 41.7802 cents 7 x 8:9 S SD: 40.3200 cents 8 x 9:11 SD: 27.6448 cents 9 x 10:12 S SD: 1.0824 cents 10 x 11:13 SD: 24.6593 cents 11 x 12:15 S SD: 24.6698 cents 12 x 13:16 SD: 22.4017 cents 13 x 14:17 SD: 32.7652 cents 14:15:16:19 SD: 26.9037 cents 15:16:17:20 SD: 20.2173 cents 16:17:18:21 S SD: 18.8546 cents 17:18:19:23 SD: 15.1327 cents 18:19:20:24 S SD: 10.8546 cents 21:22:23:28 SD: 10.7955 cents 24:25:27:32 SD: 7.5912 cents 26:27:29:35 SD: 5.4165 cents 27:28:30:36 S SD: 0.9491 cents 134:139:149:179 SD: 0.8876 cents 143:148:159:191 SD: 0.6517 cents 170:176:189:227 SD: 0.4060 cents 197:204:219:263 SD: 0.2357 cents 224:232:249:299 SD: 0.1311 cents 251:260:279:335 SD: 0.1184 cents 475:492:528:634 SD: 0.1121 cents